R.D. Sharma Solutions Class 10th: Ch 5 Trigonometric Ratios Exercise 5.1

Chapter 5 Trigonometric Ratios R.D. Sharma Solutions for Class 10th Math Exercise 5.1

Exercise 5.1

1. In each of the following one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.

(i) sinA = 2/3

Solution

(ii) cosA = 4/5

Solution

(iii) tanθ = 11

Solution

(iv) Sinθ = 11/5

Solution

(v) tanα = 5/12

Solution

(vi) Sinθ = √3/2

Solution

(vii) Cosθ = 7/25

Solution

(viii) tanθ = 8/15

Solution

(ix) cotθ = 12/5

Solution

(x) secθ = 13/5

Solution

(xi) cosecθ = √10

Solution

(xii) cosecθ = 12/5

Solution

2. In a ∆ABC, right angled at B, AB = 24 cm, BC = 7 cm. Determine
(i) Sin A, Cos A
(ii) Sin C, cos C

Solution

3. In Fig below, Find tan P and cot R. Is tan P = cot R ?

Solution

4. If sinA = 9/41, compute cosA and tanA.

Solution

5. Given 15 cot A = 8, find SinA and SecA .

Solution

6. In ∆PQR, right angled at Q, PQ = 4 cm and RQ = 3 cm. Find the values of sin P, sin R, sec P and sec R.

Solution

7. If cot θ = 7/8 , evaluate :

(i) (1+sinθ)(1-sinθ)/(1+cosθ)(1-cosθ)

(ii) cot²θ

Solution
(i)

(ii)

8. If 3 cot A = 4, check whether 1-tan² A/1+tan² A = cos² A - sin² A or not.

Solution

9. If tan θ = a/b , find the value of cosθ + sinθ/cosθ - sinθ

Solution

10. If 3 tan θ = 4 , find the value of 4cosθ - sinθ/2cosθ + sinθ

Solution

11. If 3 cot θ = 2 , find the value of 4 sinθ - 3 cosθ/2 sinθ + 6 cosθ

Solution

12. If tan θ = a/b , prove that a sin θ - b cos θ/a sin θ + b cos θ = a² - b^2/a² + b² .

Solution

13. If sec θ = 13/5, show that 2cos θ - 3cos θ/4sin θ - 9cos θ = 3.

Solution

14. If cos θ = 12/13, show that sin θ (1 - tan θ) = 35/156 .

Solution

15. If cot θ = 1/√3 , show that 1- cos² θ/2 - sin² θ = 3/5 .

Solution

16. If tan θ = 1/√7 cosec² θ - sec² θ/cosec² θ + sec² θ = 3/4 .

Solution

17. If Sec θ = 5/4 , find the value of sin θ - 2 cos θ/ tan θ - cot θ

Solution

18. If tan θ = 12/13, find the value of 2 sin θ cosθ/cos² θ - sin²θ

Solution

19. If cos θ = 3/5 , find the value of sinθ - (1/tanθ)/2 tan θ

Solution

20. If sin θ = 3/5 , evaluate cosθ - (1/tanθ)/2 cot θ

Solution

21. If tan θ = 24/7 , find that sin θ + cos θ

Solution

22. If sin θ = a/b , find sec θ + tan θ in terms of a and b .

Solution

23. If 8 tan A = 15, find sin A - cos A .

Solution

24. If tan θ = 20/21, show that 1-sin θ + cos θ/1+ sin θ + cos θ = 3/7 .

Solution

25 . If cosec A = 2 find 1/Tan A + sin A/1+cos A

Solution

26. If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.

Solution

27. In a ∆ABC, right angled at A, if tan C = √3, find the value of sin B cos C + cos B sin C.

Solution

28. State whether the following are true or false. Justify your answer.
(i) The value of tan A is always less than 1.
(ii) Sec A = 12/5 for some value of angle A.
(iii) Cos A is the abbreviation used for the cosecant of angle A.
(iv) Sin θ = 4/3 for some angle θ .

Solution